Senate Democratic Leader Chuck Schumer said Democrats had told Trump during the meeting to end the shutdown. "He resisted," Schumer said. "In fact, he said he'd keep the government closed for a very long period of time, months or even years."

Trump confirmed that comment but painted a more positive picture of the meeting, the first since a new era of divided government began when Democrats took control of the House of Representatives on Thursday.

"We had a very, very productive meeting, and we've come a long way," Trump said.

But raising the stakes in his tussle with the newly emboldened Democrats, Trump threatened extraordinary measures to build the wall, which he says is needed to stem the flow of illegal immigrants and drugs into the United States.

National emergency

Asked by a reporter whether he had considered declaring a national emergency to build the wall, Trump said: "Yes, I have ... I may do it ... But we can call a national emergency and build it very quickly."

He said he could declare a national emergency "because of the security of our country, absolutely".

The US Constitution assigns Congress the power over funding the federal government so Trump likely would face legal challenges if he tried to bypass Congress on financing the wall. Building a wall - and having Mexico pay for it - was one of Trump's main promises when he ran for president in 2016.

House Democrats suggested they would sue if Trump tries to declare a national emergency to build the wall.

"The president's authority in this area is intended for wars and genuine national emergencies," Evan Hollander, spokesman for the House Appropriations Committee, said in a statement.

"Asserting this authority to build a wasteful wall is legally dubious and would invite a legal challenge from Congress."

Douglas Holtz-Eakin, president of the American Action Forum and former director of the Congressional Budget Office, said Trump would still need Congress for the funds.

"Congress holds the purse strings," Holtz-Eakin said. "That's the essence of this dispute. He can declare a national emergency all he wants, but where's he going to get the money?"

Trump's wall project is estimated to cost about $US23 billion.

Democrats have called the wall immoral, ineffective and medieval.

Nancy Pelosi, the newly elected Democratic speaker of the House, said Friday's meeting with Trump was "sometimes contentious" but that they agreed to continue talking.

"But we recognise on the Democratic side that we really cannot resolve this until we open up government and we made that very clear to the president," she said.

Credit rating agency Moody's says the shutdown will cause minimal US economic and credit market disruption but there could be a more severe impact on financial markets and the broad economy if the closure is protracted.

A Reuters/Ipsos opinion poll last week showed that 50 per cent of the public blame Trump for the shutdown and 7 per cent blame Republican lawmakers, against 32 per cent who blame Democrats.

In a December 11 meeting with Pelosi and Schumer, Trump said he would be "proud" to shut the government over the security issue and would not blame Democrats. He has since said they are responsible.

The partial shutdown is straining the country's immigration system, worsening backlogs in courts and complicating hiring for employers.

Federal agencies such as the Justice Department, Commerce Department and departments of Agriculture, Labor, Interior and Treasury have been hit by the shutdown.

Reuters, Bloomberg